- Author:
- Nima <nafs080@aucklanduni.ac.nz>
- Date:
- 2019-07-21 09:46:02+12:00
- Desc:
- Modular version of glucose uptake model (contains water transporters and cell volume changes)
- Permanent Source URI:
- https://models.cellml.org/workspace/58c/rawfile/2ad89252015aa87ebc327c2d547bd99bc7629853/Paracellular_Dif_flux.cellml
<?xml version='1.0'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<component name="Paracellular_Diffusion">
<variable name="v_ms" public_interface="in" units="volt"/>
<variable name="Na_m" public_interface="in" units="M"/>
<variable name="K_m" public_interface="in" units="M"/>
<variable name="Cl_m" public_interface="in" units="M"/>
<variable name="Na_s" public_interface="in" units="M"/>
<variable name="K_s" public_interface="in" units="M"/>
<variable name="Cl_s" public_interface="in" units="M"/>
<!-- var CO2_m: M {pub: in};
var CO2_i: M {pub: in};-->
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="z_Na" public_interface="in" units="dimensionless"/>
<variable name="z_k" public_interface="in" units="dimensionless"/>
<variable name="z_Cl" public_interface="in" units="dimensionless"/>
<variable name="R" public_interface="in" units="J_per_K_per_mol"/>
<variable name="A_Apical" public_interface="in" units="m2"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="P_P_Na" public_interface="in" units="m_per_s"/>
<variable name="P_P_k" public_interface="in" units="m_per_s"/>
<variable name="P_P_Cl" public_interface="in" units="m_per_s"/>
<variable name="J_D_P_Na" public_interface="out" units="umol_per_s"/>
<variable name="I_D_P_Na" public_interface="out" units="uA"/>
<variable name="J_D_P_K" public_interface="out" units="umol_per_s"/>
<variable name="I_D_P_K" public_interface="out" units="uA"/>
<variable name="J_D_P_Cl" public_interface="out" units="umol_per_s"/>
<variable name="I_D_P_Cl" public_interface="out" units="uA"/>
<variable name="J_D_Paracellular" public_interface="out" units="umol_per_s"/>
<variable name="V_P_Na" public_interface="out" units="volt"/>
<variable name="V_P_K" public_interface="out" units="volt"/>
<variable name="V_P_Cl" public_interface="out" units="volt"/>
<variable initial_value="10" name="G_P_Na" public_interface="out" units="S_per_m2"/>
<variable initial_value="1" name="G_P_K" public_interface="out" units="S_per_m2"/>
<variable initial_value="4" name="G_P_Cl" public_interface="out" units="S_per_m2"/>
<!-- var I_D_P_CO2: uA {pub: out};
var J_D_P_CO2: umol_per_s {pub: out};
var G_P_CO2: S_per_m2 {init: 7, pub: out};
var v_P_CO2: volt {pub: out};-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_P_Na</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<ci>z_Na</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Na_m</ci>
<ci>Na_s</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_D_P_Na</ci>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>6</cn>
</apply>
<ci>G_P_Na</ci>
<ci>A_Apical</ci>
<apply>
<minus/>
<ci>v_ms</ci>
<ci>V_P_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_D_P_Na</ci>
<apply>
<divide/>
<ci>I_D_P_Na</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>V_P_K</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<ci>z_k</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>K_m</ci>
<ci>K_s</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_D_P_K</ci>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>6</cn>
</apply>
<ci>G_P_K</ci>
<ci>A_Apical</ci>
<apply>
<minus/>
<ci>v_ms</ci>
<ci>V_P_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_D_P_K</ci>
<apply>
<divide/>
<ci>I_D_P_K</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>V_P_Cl</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<ci>z_Cl</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Cl_m</ci>
<ci>Cl_s</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_D_P_Cl</ci>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>6</cn>
</apply>
<ci>G_P_Cl</ci>
<ci>A_Apical</ci>
<apply>
<minus/>
<ci>v_ms</ci>
<ci>V_P_Cl</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_D_P_Cl</ci>
<apply>
<divide/>
<ci>I_D_P_Cl</ci>
<ci>F</ci>
</apply>
</apply>
<!-- v_P_CO2 = R*T/F*ln(CO2_m/CO2_i);
I_D_P_CO2 = 1e6{dimensionless}*G_P_CO2*A_cell*(v_ms-v_P_CO2);
J_D_P_CO2 = I_D_P_CO2/F;-->
<apply>
<eq/>
<ci>J_D_Paracellular</ci>
<apply>
<plus/>
<ci>J_D_P_Na</ci>
<ci>J_D_P_K</ci>
<ci>J_D_P_Cl</ci>
</apply>
</apply>
</math>
</component>
</model>
